The hmatrix-nipals package

NIPALS -- Nonlinear Iterative Partial Least Squares
http://en.wikipedia.org/wiki/NIPALS, is a method for iteratively
finding the left singular vectors of a large matrix. In other words
it discovers the largest principal component
http://en.wikipedia.org/wiki/Principal_component of a set of
mean-centred samples, along with the score (the magnitude of the
principal component) for each sample, and the residual of each
sample that is orthogonal to the principal component. By repeating
the procedure on the residuals, the second principal component is
found, and so on.

The advantage of NIPALS over more traditional methods, like SVD, is
that it is memory efficient, and can complete early if only a small
number of principal components are needed. It is also simple to
implement correctly. Additionally, because it doesn't pre-condition
the sample matrix in any way, it can be implemented with only two
sequential passes per iteration through the sample data, which is
much more efficient than random accesses if the data-set is too
large to fit in memory.

NIPALS is not generally recommended because sample matrices where
the largest eigenvalues are close in magnitude will cause NIPALS to
converge very slowly. In general, Lanczos methods
http://en.wikipedia.org/wiki/Lanczos_algorithm or some other
truncated singular value decomposition algorithm are preferred to
NIPALS because of this convergence issue, but these methods often
require the sample matrix to fit in memory, or store large
conditioning matrices, which isn't always feasible. However, if you
know of free and memory-efficient implementations of these more
sophisticated algorithms, please contact the author with a pointer.